Divide the polynomials.
Explanation: Usually, there are many different ways to divide polynomials. Here, we will use the method of polynomial long division. $\begin{array}{r} x+\phantom{1}5 \\ x+2|\overline{x^2+7x+12} \\ \mathllap{-(}\underline{x^2+2x\phantom{+12}\rlap )} \\ 5x+12 \\ \mathllap{-(}\underline{5x+10\rlap )} \\ 2 \end{array}$ We get that the quotient is $x+5$ and the remainder is $2$, and therefore: $\dfrac{x^2+7x+12}{x+2}=x+5+\dfrac{2}{x+2}$ [I want to see a different way of performing the division.]